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Each person attending a party was charged the same admission

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Each person attending a party was charged the same admission [#permalink] New post 09 Nov 2012, 06:28
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Question Stats:

81% (02:12) correct 19% (00:41) wrong based on 32 sessions
Each person attending a party was charged the same admission fee. How many people attended the party?

(1) If the fee had been 0.75$ less and 100 more people had attended, the club would have made the same amount of money.
(2) If the fee had been 1.50$ more and 100 fewer people had attended, the club would have made the same amount of money.

I have a specific question regarding this problem :

Obviously Statement 1 and 2 are insufficient alone, however once we find out equation 1: xy = (x-3/4)(y+100) from statement 1 and xy = (x+3/2)(y-100) from statement 2, why can't we simply equate them?
(x-3/4)(y+100) = (x+3/2)(y-100)

I'd appreciate any help! Thanks
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Nov 2012, 06:32, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Each person attending a party was charged the same admission [#permalink] New post 09 Nov 2012, 06:43
Expert's post
mockney wrote:
Each person attending a party was charged the same admission fee. How many people attended the party?

(1) If the fee had been 0.75$ less and 100 more people had attended, the club would have made the same amount of money.
(2) If the fee had been 1.50$ more and 100 fewer people had attended, the club would have made the same amount of money.

I have a specific question regarding this problem :

Obviously Statement 1 and 2 are insufficient alone, however once we find out equation 1: xy = (x-3/4)(y+100) from statement 1 and xy = (x+3/2)(y-100) from statement 2, why can't we simply equate them?
(x-3/4)(y+100) = (x+3/2)(y-100)

I'd appreciate any help! Thanks


Well, actually you can: (x-3/4)(y+100) = (x+3/2)(y-100) --> 9y=800x+300.

From xy = (x-3/4)(y+100) we'll have that 3y=400x-300, so 9y=1200x-900. Equating again: 800x+300=1200x-900 --> x=3 --> y=300.

Though you can directly simplify xy = (x-3/4)(y+100) to get 3y=400x-300 and xy = (x+3/2)(y-100) to get 3y=200x+300 --> 400x-300=200x+300 --> x=3 --> y=300.

Hope it's clear.

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Re: Each person attending a party was charged the same admission [#permalink] New post 09 Nov 2012, 06:54
Thank you Bunuel for your help!
I was just expecting to find a value for either x or y directly without needing to isolate for y from one of the 2 equations!
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Re: Each person attending a party was charged the same admission [#permalink] New post 15 Nov 2012, 02:41
WE NEed to show that the two equatin is not the same. but I do not know how to do. pls, help

we can avoid much computation.
Re: Each person attending a party was charged the same admission   [#permalink] 15 Nov 2012, 02:41
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